Viscous shear stress at the outer mudcake boundary

Input(s)

$R_{c}$: Radius from the Center of Drillpipe to the beginning of Mudcake (in.)

$R_{p}$: Radius from the Center to the Inner Boundary of the Drillpipe (in.)

$v_{z}$: Axial Velocity Parallel to the Wellbore Axis (in/s)

$x_{f}$: Transient Invasion Front (in.)

$x_{f, o}$: Initial Displacement, i.e., Spurt (in.)

$\frac{d p}{d z}$: Pressure change with $\mathrm{Z}$ direction that is parallel to the Wellbore Axis (psi/in.)

$\mu$: Viscosity $(\mathrm{cP})$

Output(s)

$\tau_{(R c)}$: Viscous Shear Stress at the outer Mudcake boundary (lb/in. ${ }^{2}$ )

Formula(s)

$$ \begin{gathered} \tau_{(R c)}=\mu\left(d v_{z} / d r\right)_{(R c)} \\ \tau_{(R c)}=\frac{1}{4}\left[2 R_{c}+\left\{\left(R_{c}^{2}-R_{p}^{2}\right) /\left(R_{c} \log \left(R_{p} / R_{c}\right)\right)\right\}\right] \frac{d p}{d z} \end{gathered} $$

Reference(s)

Chin, W. C. (1995). Formation Invasion, Page: 59.